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Enable G be a in the neighborhood K-proper workforce, S ∈ Syl_5(G), and Z = Z(S). We demonstratethat if is 5-constrained and Z isn't weakly closed in thenG is isomorphic to the monster sporadic uncomplicated staff.

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1, two waves propagate in opposite directions parallel to the x axis. The impedance Z(M1 ) at M1 is known. 1 Plane waves propagate both in the x direction and in the opposite direction. The impedance at M1 is Z(M1 ). 16) where d is equal to x(M1 ) − x(M2 ). 16) is known as the impedance translation theorem. 2. Two points M2 and M3 are shown at the boundary of ﬂuids 1 and 2, M3 being in ﬂuid 2 and M2 in ﬂuid 1. 2 A layer of ﬂuid of ﬁnite thickness in contact with another ﬂuid on its front face and backed by a rigid impervious wall on its rear face.

Z(M1 ) is the impedance of the air gap. 47) Zc = Zo where Zc is the characteristic impedance in air. 8 shows the result for the second conﬁguration. 9. It may be noted that as in the case for normal incidence, pressures, velocities and impedances are individually equal at either side of the boundary between air and the ﬂuid equivalent to the porous material; however, due to the variation of the characteristic impedance, the reﬂection and absorption coefﬁcients are different. 5, ﬁbrous materials such as ﬁbreglass are anisotropic (Nicolas and Berry 1984, Allard et al.

The impedance Z(M1 ) at M1 is known. 1 Plane waves propagate both in the x direction and in the opposite direction. The impedance at M1 is Z(M1 ). 16) where d is equal to x(M1 ) − x(M2 ). 16) is known as the impedance translation theorem. 2. Two points M2 and M3 are shown at the boundary of ﬂuids 1 and 2, M3 being in ﬂuid 2 and M2 in ﬂuid 1. 2 A layer of ﬂuid of ﬁnite thickness in contact with another ﬂuid on its front face and backed by a rigid impervious wall on its rear face. 3 Three layers of ﬂuid backed by an impedance plane II.